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authorValentin Popov <valentin@popov.link>2024-07-19 15:37:58 +0300
committerValentin Popov <valentin@popov.link>2024-07-19 15:37:58 +0300
commita990de90fe41456a23e58bd087d2f107d321f3a1 (patch)
tree15afc392522a9e85dc3332235e311b7d39352ea9 /vendor/num-integer/src/roots.rs
parent3d48cd3f81164bbfc1a755dc1d4a9a02f98c8ddd (diff)
downloadfparkan-a990de90fe41456a23e58bd087d2f107d321f3a1.tar.xz
fparkan-a990de90fe41456a23e58bd087d2f107d321f3a1.zip
Deleted vendor folder
Diffstat (limited to 'vendor/num-integer/src/roots.rs')
-rw-r--r--vendor/num-integer/src/roots.rs391
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diff --git a/vendor/num-integer/src/roots.rs b/vendor/num-integer/src/roots.rs
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@@ -1,391 +0,0 @@
-use core;
-use core::mem;
-use traits::checked_pow;
-use traits::PrimInt;
-use Integer;
-
-/// Provides methods to compute an integer's square root, cube root,
-/// and arbitrary `n`th root.
-pub trait Roots: Integer {
- /// Returns the truncated principal `n`th root of an integer
- /// -- `if x >= 0 { ⌊ⁿ√x⌋ } else { ⌈ⁿ√x⌉ }`
- ///
- /// This is solving for `r` in `rⁿ = x`, rounding toward zero.
- /// If `x` is positive, the result will satisfy `rⁿ ≤ x < (r+1)ⁿ`.
- /// If `x` is negative and `n` is odd, then `(r-1)ⁿ < x ≤ rⁿ`.
- ///
- /// # Panics
- ///
- /// Panics if `n` is zero:
- ///
- /// ```should_panic
- /// # use num_integer::Roots;
- /// println!("can't compute ⁰√x : {}", 123.nth_root(0));
- /// ```
- ///
- /// or if `n` is even and `self` is negative:
- ///
- /// ```should_panic
- /// # use num_integer::Roots;
- /// println!("no imaginary numbers... {}", (-1).nth_root(10));
- /// ```
- ///
- /// # Examples
- ///
- /// ```
- /// use num_integer::Roots;
- ///
- /// let x: i32 = 12345;
- /// assert_eq!(x.nth_root(1), x);
- /// assert_eq!(x.nth_root(2), x.sqrt());
- /// assert_eq!(x.nth_root(3), x.cbrt());
- /// assert_eq!(x.nth_root(4), 10);
- /// assert_eq!(x.nth_root(13), 2);
- /// assert_eq!(x.nth_root(14), 1);
- /// assert_eq!(x.nth_root(std::u32::MAX), 1);
- ///
- /// assert_eq!(std::i32::MAX.nth_root(30), 2);
- /// assert_eq!(std::i32::MAX.nth_root(31), 1);
- /// assert_eq!(std::i32::MIN.nth_root(31), -2);
- /// assert_eq!((std::i32::MIN + 1).nth_root(31), -1);
- ///
- /// assert_eq!(std::u32::MAX.nth_root(31), 2);
- /// assert_eq!(std::u32::MAX.nth_root(32), 1);
- /// ```
- fn nth_root(&self, n: u32) -> Self;
-
- /// Returns the truncated principal square root of an integer -- `⌊√x⌋`
- ///
- /// This is solving for `r` in `r² = x`, rounding toward zero.
- /// The result will satisfy `r² ≤ x < (r+1)²`.
- ///
- /// # Panics
- ///
- /// Panics if `self` is less than zero:
- ///
- /// ```should_panic
- /// # use num_integer::Roots;
- /// println!("no imaginary numbers... {}", (-1).sqrt());
- /// ```
- ///
- /// # Examples
- ///
- /// ```
- /// use num_integer::Roots;
- ///
- /// let x: i32 = 12345;
- /// assert_eq!((x * x).sqrt(), x);
- /// assert_eq!((x * x + 1).sqrt(), x);
- /// assert_eq!((x * x - 1).sqrt(), x - 1);
- /// ```
- #[inline]
- fn sqrt(&self) -> Self {
- self.nth_root(2)
- }
-
- /// Returns the truncated principal cube root of an integer --
- /// `if x >= 0 { ⌊∛x⌋ } else { ⌈∛x⌉ }`
- ///
- /// This is solving for `r` in `r³ = x`, rounding toward zero.
- /// If `x` is positive, the result will satisfy `r³ ≤ x < (r+1)³`.
- /// If `x` is negative, then `(r-1)³ < x ≤ r³`.
- ///
- /// # Examples
- ///
- /// ```
- /// use num_integer::Roots;
- ///
- /// let x: i32 = 1234;
- /// assert_eq!((x * x * x).cbrt(), x);
- /// assert_eq!((x * x * x + 1).cbrt(), x);
- /// assert_eq!((x * x * x - 1).cbrt(), x - 1);
- ///
- /// assert_eq!((-(x * x * x)).cbrt(), -x);
- /// assert_eq!((-(x * x * x + 1)).cbrt(), -x);
- /// assert_eq!((-(x * x * x - 1)).cbrt(), -(x - 1));
- /// ```
- #[inline]
- fn cbrt(&self) -> Self {
- self.nth_root(3)
- }
-}
-
-/// Returns the truncated principal square root of an integer --
-/// see [Roots::sqrt](trait.Roots.html#method.sqrt).
-#[inline]
-pub fn sqrt<T: Roots>(x: T) -> T {
- x.sqrt()
-}
-
-/// Returns the truncated principal cube root of an integer --
-/// see [Roots::cbrt](trait.Roots.html#method.cbrt).
-#[inline]
-pub fn cbrt<T: Roots>(x: T) -> T {
- x.cbrt()
-}
-
-/// Returns the truncated principal `n`th root of an integer --
-/// see [Roots::nth_root](trait.Roots.html#tymethod.nth_root).
-#[inline]
-pub fn nth_root<T: Roots>(x: T, n: u32) -> T {
- x.nth_root(n)
-}
-
-macro_rules! signed_roots {
- ($T:ty, $U:ty) => {
- impl Roots for $T {
- #[inline]
- fn nth_root(&self, n: u32) -> Self {
- if *self >= 0 {
- (*self as $U).nth_root(n) as Self
- } else {
- assert!(n.is_odd(), "even roots of a negative are imaginary");
- -((self.wrapping_neg() as $U).nth_root(n) as Self)
- }
- }
-
- #[inline]
- fn sqrt(&self) -> Self {
- assert!(*self >= 0, "the square root of a negative is imaginary");
- (*self as $U).sqrt() as Self
- }
-
- #[inline]
- fn cbrt(&self) -> Self {
- if *self >= 0 {
- (*self as $U).cbrt() as Self
- } else {
- -((self.wrapping_neg() as $U).cbrt() as Self)
- }
- }
- }
- };
-}
-
-signed_roots!(i8, u8);
-signed_roots!(i16, u16);
-signed_roots!(i32, u32);
-signed_roots!(i64, u64);
-#[cfg(has_i128)]
-signed_roots!(i128, u128);
-signed_roots!(isize, usize);
-
-#[inline]
-fn fixpoint<T, F>(mut x: T, f: F) -> T
-where
- T: Integer + Copy,
- F: Fn(T) -> T,
-{
- let mut xn = f(x);
- while x < xn {
- x = xn;
- xn = f(x);
- }
- while x > xn {
- x = xn;
- xn = f(x);
- }
- x
-}
-
-#[inline]
-fn bits<T>() -> u32 {
- 8 * mem::size_of::<T>() as u32
-}
-
-#[inline]
-fn log2<T: PrimInt>(x: T) -> u32 {
- debug_assert!(x > T::zero());
- bits::<T>() - 1 - x.leading_zeros()
-}
-
-macro_rules! unsigned_roots {
- ($T:ident) => {
- impl Roots for $T {
- #[inline]
- fn nth_root(&self, n: u32) -> Self {
- fn go(a: $T, n: u32) -> $T {
- // Specialize small roots
- match n {
- 0 => panic!("can't find a root of degree 0!"),
- 1 => return a,
- 2 => return a.sqrt(),
- 3 => return a.cbrt(),
- _ => (),
- }
-
- // The root of values less than 2ⁿ can only be 0 or 1.
- if bits::<$T>() <= n || a < (1 << n) {
- return (a > 0) as $T;
- }
-
- if bits::<$T>() > 64 {
- // 128-bit division is slow, so do a bitwise `nth_root` until it's small enough.
- return if a <= core::u64::MAX as $T {
- (a as u64).nth_root(n) as $T
- } else {
- let lo = (a >> n).nth_root(n) << 1;
- let hi = lo + 1;
- // 128-bit `checked_mul` also involves division, but we can't always
- // compute `hiⁿ` without risking overflow. Try to avoid it though...
- if hi.next_power_of_two().trailing_zeros() * n >= bits::<$T>() {
- match checked_pow(hi, n as usize) {
- Some(x) if x <= a => hi,
- _ => lo,
- }
- } else {
- if hi.pow(n) <= a {
- hi
- } else {
- lo
- }
- }
- };
- }
-
- #[cfg(feature = "std")]
- #[inline]
- fn guess(x: $T, n: u32) -> $T {
- // for smaller inputs, `f64` doesn't justify its cost.
- if bits::<$T>() <= 32 || x <= core::u32::MAX as $T {
- 1 << ((log2(x) + n - 1) / n)
- } else {
- ((x as f64).ln() / f64::from(n)).exp() as $T
- }
- }
-
- #[cfg(not(feature = "std"))]
- #[inline]
- fn guess(x: $T, n: u32) -> $T {
- 1 << ((log2(x) + n - 1) / n)
- }
-
- // https://en.wikipedia.org/wiki/Nth_root_algorithm
- let n1 = n - 1;
- let next = |x: $T| {
- let y = match checked_pow(x, n1 as usize) {
- Some(ax) => a / ax,
- None => 0,
- };
- (y + x * n1 as $T) / n as $T
- };
- fixpoint(guess(a, n), next)
- }
- go(*self, n)
- }
-
- #[inline]
- fn sqrt(&self) -> Self {
- fn go(a: $T) -> $T {
- if bits::<$T>() > 64 {
- // 128-bit division is slow, so do a bitwise `sqrt` until it's small enough.
- return if a <= core::u64::MAX as $T {
- (a as u64).sqrt() as $T
- } else {
- let lo = (a >> 2u32).sqrt() << 1;
- let hi = lo + 1;
- if hi * hi <= a {
- hi
- } else {
- lo
- }
- };
- }
-
- if a < 4 {
- return (a > 0) as $T;
- }
-
- #[cfg(feature = "std")]
- #[inline]
- fn guess(x: $T) -> $T {
- (x as f64).sqrt() as $T
- }
-
- #[cfg(not(feature = "std"))]
- #[inline]
- fn guess(x: $T) -> $T {
- 1 << ((log2(x) + 1) / 2)
- }
-
- // https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
- let next = |x: $T| (a / x + x) >> 1;
- fixpoint(guess(a), next)
- }
- go(*self)
- }
-
- #[inline]
- fn cbrt(&self) -> Self {
- fn go(a: $T) -> $T {
- if bits::<$T>() > 64 {
- // 128-bit division is slow, so do a bitwise `cbrt` until it's small enough.
- return if a <= core::u64::MAX as $T {
- (a as u64).cbrt() as $T
- } else {
- let lo = (a >> 3u32).cbrt() << 1;
- let hi = lo + 1;
- if hi * hi * hi <= a {
- hi
- } else {
- lo
- }
- };
- }
-
- if bits::<$T>() <= 32 {
- // Implementation based on Hacker's Delight `icbrt2`
- let mut x = a;
- let mut y2 = 0;
- let mut y = 0;
- let smax = bits::<$T>() / 3;
- for s in (0..smax + 1).rev() {
- let s = s * 3;
- y2 *= 4;
- y *= 2;
- let b = 3 * (y2 + y) + 1;
- if x >> s >= b {
- x -= b << s;
- y2 += 2 * y + 1;
- y += 1;
- }
- }
- return y;
- }
-
- if a < 8 {
- return (a > 0) as $T;
- }
- if a <= core::u32::MAX as $T {
- return (a as u32).cbrt() as $T;
- }
-
- #[cfg(feature = "std")]
- #[inline]
- fn guess(x: $T) -> $T {
- (x as f64).cbrt() as $T
- }
-
- #[cfg(not(feature = "std"))]
- #[inline]
- fn guess(x: $T) -> $T {
- 1 << ((log2(x) + 2) / 3)
- }
-
- // https://en.wikipedia.org/wiki/Cube_root#Numerical_methods
- let next = |x: $T| (a / (x * x) + x * 2) / 3;
- fixpoint(guess(a), next)
- }
- go(*self)
- }
- }
- };
-}
-
-unsigned_roots!(u8);
-unsigned_roots!(u16);
-unsigned_roots!(u32);
-unsigned_roots!(u64);
-#[cfg(has_i128)]
-unsigned_roots!(u128);
-unsigned_roots!(usize);